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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.constants_intro"></a><a class="link" href="constants_intro.html" title="Introduction">Introduction</a>
</h2></div></div></div>
<p>
      Boost.Math provides a collection of mathematical constants.
    </p>
<h5>
<a name="math_toolkit.constants_intro.h0"></a>
      <span class="phrase"><a name="math_toolkit.constants_intro.why_use_boost_math_mathematical_"></a></span><a class="link" href="constants_intro.html#math_toolkit.constants_intro.why_use_boost_math_mathematical_">Why
      use Boost.Math mathematical constants?</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<p class="simpara">
          Readable. For the very many jobs just using built-in like <code class="computeroutput"><span class="keyword">double</span></code>, you can just write expressions like
        </p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">area</span> <span class="special">=</span> <span class="identifier">pi</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span></pre>
<p class="simpara">
          (If that's all you want, jump direct to <a class="link" href="tutorial/non_templ.html" title="Use in non-template code">use
          in non-template code</a>!)
        </p>
</li>
<li class="listitem">
          Effortless - avoiding a search of reference sources.
        </li>
<li class="listitem">
          Usable with both builtin floating point types, and user-defined, possibly
          extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter
          case the constants are computed to the necessary precision and then cached.
        </li>
<li class="listitem">
          Accurate - ensuring that the values are as accurate as possible for the
          chosen floating-point type
          <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
<li class="listitem">
                No loss of accuracy from repeated rounding of intermediate computations.
              </li>
<li class="listitem">
                Result is computed with higher precision and only rounded once.
              </li>
<li class="listitem">
                Less risk of inaccurate result from functions pow, trig and log at
                <a href="http://en.wikipedia.org/wiki/Corner_case" target="_top">corner cases</a>.
              </li>
<li class="listitem">
                Less risk of <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" target="_top">cancellation
                error</a>.
              </li>
</ul></div>
        </li>
<li class="listitem">
          Portable - as possible between different systems using different floating-point
          precisions: see <a class="link" href="tutorial/templ.html" title="Use in template code">use in template
          code</a>.
        </li>
<li class="listitem">
          Tested - by comparison with other published sources, or separately computed
          at long double precision.
        </li>
<li class="listitem">
<p class="simpara">
          Faster - can avoid (re-)calculation at runtime.
          <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
<li class="listitem">
                If the value returned is a builtin type then it's returned by value
                as a <code class="computeroutput"><span class="keyword">constexpr</span></code> (C++11
                feature, if available).
              </li>
<li class="listitem">
                If the value is computed and cached (or constructed from a string
                representation and cached), then it's returned by constant reference.
              </li>
</ul></div>
        </p>
<p class="simpara">
          This can be significant if:
        </p>
<p class="simpara">
          <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
<li class="listitem">
                Functions pow, trig or log are used.
              </li>
<li class="listitem">
                Inside an inner loop.
              </li>
<li class="listitem">
                Using a high-precision UDT like <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>.
              </li>
<li class="listitem">
                Compiler optimizations possible with built-in types, especially
                <code class="computeroutput"><span class="keyword">double</span></code>, are not available.
              </li>
</ul></div>
        </p>
</li>
</ul></div>
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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